The need to incorporate communities in compartmental models

Tian et al. provide a framework for assessing populationlevel interventions of disease outbreaks through the construction of counterfactuals in a large-scale, natural experiment assessing the efficacy of mild, but early interventions compared to delayed interventions. The technique is applied to the recent SARS-CoV-2 outbreak with the population of Shenzhen, China acting as the mild-but-early treatment group and a combination of several US counties resembling Shenzhen but enacting a delayed intervention acting as the control. To help further the development of this framework and identify an avenue for further enhancement, we focus on the use and potential limitations of compartmental models. In particular, compartmental models make assumptions about the communicability of a disease that may not perform well when they are used for large areas with multiple communities where movement is restricted. To illustrate this phenomena, we provide a simulation of a directed percolation (outbreak) process on a simple stochastic block model with two blocks. The simulations show that when transmissibility between two communities is severely restricted an outbreak in two communities resembles a primary and secondary outbreak potentially causing policy and decision makers to mistake effective intervention strategies with noncompliance or inefficacy of an intervention.

Keywords

stochastic block model, SIHR compartmental model, directed percolation

2010 Mathematics Subject Classification

Primary 37M05. Secondary 62P10.

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This work was partially supported by the National Science Foundation (NSF) Grant Human Networks and Data Science - Infrastructure (HNDS-I), award numbers 2024335 and 2024233.

Received 10 October 2020

Accepted 16 October 2020

Published 18 December 2020